A297214 Expansion of e.g.f. exp(cos(sin(x))-1) (even powers only).

1, -1, 8, -127, 3523, -146964, 8538477, -655457233, 63974756924, -7713566822979, 1123255462229507, -193995005614903728, 39147722262966666217, -9115873617718182207793, 2423565558533387761866928, -728969374928760685473620951, 246100624914698937364249220851

Offset: 0

Author

Ilya Gutkovskiy, Dec 27 2017

Keywords

• sign

Examples

			exp(cos(sin(x))-1) = 1 - x^2/2! + 8*x^4/4! - 127*x^6/6! + 3523*x^8/8! - 146964*x^10/10! + ...
		

Crossrefs

Cf. A003709, A009045, A009201, A009202, A009203, A009204, A009238, A009239, A009240, A009241, A009254, A297215.

Programs

Mathematica

nmax = 16; Table[(CoefficientList[Series[Exp[Cos[Sin[x]] - 1], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]

Formula

a(n) = (2*n)! * [x^(2*n)] exp(cos(sin(x))-1).